Finite Group Databasebeta

← C2×#14521221 #16855046

Subgroups — C2×#14521221 #16855046

Order 3968.

728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758564C211yesmaximal, characteristic, complemented
2C2×#11758509C212yesmaximal, complemented
3#14521221C218yesmaximal, direct product factor
4C2×#11758393C212yesmaximal, complemented
5C2×#11758424C211yesmaximal, characteristic, complemented
6C2×C31×#124C211yesmaximal, characteristic, complemented
7C22×Q8×C31C2211yescharacteristic
8C22×D4×C31C2211yescharacteristic
9#11758564—22no—
10#11758564—24no—
11#11758564C2214yescomplemented
12C2×#92499—22no—
13C2×Q8×D31—22no—
14C2×#92495—22no—
15C2×#92495C2212yes—
16C31×#124—22no—
17C31×#124C2214yescomplemented
18C2×C22⋊C4×C31—22no—
19C2×C42×C31C2211yescharacteristic
20C2×#92480—22no—
21#11758509—24no—
22#11758509C2218yescomplemented
23C2×#92479—22no—
24C2×#92474C2212yes—
25#11758424C2214yescomplemented
26#11758393C2218yescomplemented
27C24×C31—21no—
28C2×Q8×C31—22no—
29C2×Q8×C31—22no—
30C2×Q8×C31D412yes—
31C2×Q8×C31C2312yes—
32C2×D4×C31—22no—
33C2×D4×C31—22no—
34C2×D4×C31—21no—
35C2×D4×C31C2312yes—
36C22×C4×C31—21no—
37C22×C4×C31D412yes—
38C22×C4×C31C2311yescharacteristic
39C2×C22⋊D31—22no—
40#92499—28no—
41#92499—28no—
42Q8×D31—28no—
43Q8×D31—28no—
44#92495—28no—
45#92495—28no—
46#92495—22no—
47#92495—22no—
48#92495D414yes—
49#92495C2314yes—
50C2×D124—22no—
51C2×D124D412yes—
52C2×C4×D31—24no—
53C2×C4×D31—22no—
54C2×Dic62—22no—
55C2×Dic62D412yes—
56C22⋊C4×C31—28no—
57C42×C31—21no—
58C42×C31C2312yes—
59#92480—28no—
60#92479—28no—
61#92474—22no—
62#92474C2314yes—
63C2×C31⋊C8—22no—
64C23×C31—22no—
65C23×C31—44no—
66C23×C31—41no—
67C23×C31—41no—
68C23×C31C2×D411yescharacteristic
69C22×D31—22no—
70Q8×C31—24no—
71Q8×C31—24no—
72D4×C31—24no—
73D4×C31—42no—
74C2×C4×C31—22no—
75C2×C4×C31—22no—
76C2×C4×C31—22no—
77C2×C4×C31—42no—
78C2×C4×C31C2×D412yes—
79C2×C4×C31C2×D412yes—
80C2×C4×C31C2×D414yes—
81C2×C4×C31C2×D411yescharacteristic
82C2×C4×C31C2411yescharacteristic
83C22⋊D31—24no—
84C22⋊D31—24no—
85C2×Dic31—22no—
86D124—28no—
87D124—22no—
88D124C2×D414yes—
89C4×D31—216no—
90C4×D31—24no—
91C4×D31—24no—
92Dic62—28no—
93Dic62—22no—
94Dic62C2×D414yes—
95C31⋊C8—24no—
96C2×#454—311nomaximal, Sylow
97C22×C31—22no—
98C22×C31—44no—
99C22×C31—42no—
100C22×C31—82no—
101C22×C31—82no—
102C22×C31#12011yescharacteristic
103C22×C31#12011yescharacteristic
104C22×C31C22×D411yescharacteristic
105C2×D31—24no—
106C2×D31—44no—
107C4×C31—24no—
108C4×C31—42no—
109C4×C31#12012yes—
110C4×C31C22×D412yes—
111Dic31—24no—
112C2×2−1+4—311no—
113C2×AGL(1,ℤ/8)—312no—
114C2×#124D3111yescharacteristic, complemented
115#454—318no—
116C2×#104—312no—
117C2×#101—311no—
118C2×C31—21no—
119C2×C31—21no—
120C2×C31—82no—
121C2×C31#45412yescomplemented
122C2×C31C2×#12011yescharacteristic
123D31—44no—
1242−1+4—314no—
1252−1+4—624no—
1262−1+4—622no—
127C2×#41—312no—
128C2×#41—622no—
129C2×#41—622no—
130C22×Q8—622no—
131C22×Q8C2×D3111yescharacteristic
132C22×D4C2×D3111yescharacteristic
133AGL(1,ℤ/8)—318no—
134AGL(1,ℤ/8)—624no—
135C2×SD16—622no—
136C2×D8—622no—
137C2×M16—312no—
138#124—22no—
139#124C2×D3114yescomplemented
140C2×C22⋊C4—22no—
141C2×C42C2×D3111yescharacteristic
142#104—318no—
143#101—314no—
144C31C2×#45411yescharacteristic, complemented, Sylow
145C24—21no—
146#41—314no—
147#41—314no—
148#41—628no—
149#41—628no—
150#41—628no—
151#41—622no—
152#41—622no—
153#41—628no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—312no—
157C2×Q8—622no—
158C2×Q8—628no—
159C2×Q8—628no—
160C2×Q8C22⋊D3112yes—
161C2×Q8C22×D3112yes—
162C2×D4—22no—
163C2×D4—22no—
164C2×D4—21no—
165C2×D4—312no—
166C2×D4—622no—
167C2×D4—622no—
168C2×D4C22×D3112yes—
169C22×C4—21no—
170C22×C4—624no—
171C22×C4—622no—
172C22×C4C22⋊D3112yes—
173C22×C4C22×D3111yescharacteristic
174SD16—628no—
175D8—628no—
176M16—314no—
177M16—622no—
178C2×C8—622no—
179C22⋊C4—28no—
180C42—21no—
181C42C22×D3112yes—
182C23—22no—
183C23—44no—
184C23—41no—
185C23—41no—
186C23—622no—
187C23C2×C22⋊D3111yescharacteristic
188Q8—24no—
189Q8—24no—
190Q8—314no—
191Q8—628no—
192Q8—622no—
193D4—24no—
194D4—42no—
195D4—314no—
196D4—628no—
197D4—624no—
198D4—624no—
199D4—622no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—42no—
204C2×C4—6216no—
205C2×C4—622no—
206C2×C4—624no—
207C2×C4—624no—
208C2×C4D4×D3112yes—
209C2×C4D4×D3112yes—
210C2×C4C2×C22⋊D3114yes—
211C2×C4C2×C22⋊D3111yescharacteristic
212C2×C4C23×D3111yescharacteristic
213C8—624no—
214C22—22no—
215C22—44no—
216C22—42no—
217C22—82no—
218C22—82no—
219C22—624no—
220C22—1244no—
221C22#1175851411yescharacteristic
222C22#1175851411yescharacteristic
223C22C22×C22⋊D3111yescharacteristic
224C4—24no—
225C4—42no—
226C4—624no—
227C4#1175851412yes—
228C4C2×D4×D3112yes—
229C2—21no—
230C2—21no—
231C2—82no—
232C2—1244no—
233C2#1452122112yesdirect product factor
234C2C2×#1175851411yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#124C2
socleC22×C31#120
hypercenterC2×#124D31
hypocenterC31C2×#454
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11758564C2semidirect
2. C2×#11758509C2semidirect
3. #14521221C2direct (N × H)
4. C2×#11758393C2semidirect
5. C2×#11758424C2semidirect
6. C2×C31×#124C2semidirect
11. #11758564C22semidirect
17. C31×#124C22semidirect
22. #11758509C22semidirect
25. #11758424C22semidirect
26. #11758393C22semidirect
114. C2×#124D31semidirect
121. C2×C31#454semidirect
139. #124C2×D31semidirect
144. C31C2×#454semidirect
233. C2#14521221direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117585642
C2×#117585092
#145212212
C2×#117583932
C2×#117584242
C2×C31×#1242
C2×#45431